onsider that, we have the following initial value problem: y' = et-y, y(0) = 1, 0

Q: 1 4. ,2x+7

A: Note: As there are three different questions, according to policy of our company we will solve the…

Q: A rock is thrown upward from a bridge that is 53 feet above a road. The rock reaches its maximum…

A: Solved below

Q: Exercise 3. Use the properties of definite integral in the following: a) If f f(x)dx = 12, and…

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Q: JA di is concave downward. Find the interval on which the curve x) - 6+ 8t

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Q: Determine the simple interest. (The rate is an annual rate unless otherwise stated. Assume 360 days…

A: P= $ 675 r= 7.75%= 0.0775 t= 30 days Since the rate of interest is given per year. Therefore, Time…

Q: Assessment Identify whether the following functions are continuous or not. Write your solutions on a…

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Q: Determine the convergence or divergence of the series. (If you need to use co or -00, enter INFINITY…

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Q: 2.25 † Let I" -a" if x + a, f(x) = I-a if x = a, where n e N. Find the value of e that makes f E…

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Q: Find the taylor series being centered at the given values of a (use the known n series) f(x) = x…

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Q: Test the series below for convergence using the Ratio Test. S In(n) 6h n=2 The limit of the ratio…

A: Given: Now,             limn→∞ lnn+16n+1lnn6n=limn→∞ lnn+16n· 6lnn6n=16·limn→∞…

Q: Evaluate the definite integrals using the graph of f (x) below. 6- 4- 2- 4 6. 10 12 -2- -4- -6 3 (a)…

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Q: T 15 dx The integral is equal to

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Q: A company invests $19,000 to produce a product that will sell for $56.85. Each unit costs $9.20 to…

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Q: The size P of a certain insect population at time t (in days) obeys the function P(t) = 100 e 0.09t…

A: In multiple question we are allowed to answer only first three sub parts

Q: Find an equation of a line that is tangent to the graph of fand parallel to the given line. Function…

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Q: Test the series below for convergence using the Root Test. 5 (5n + 4 2n + 1 n=1 The limit of the…

A: This is a problem related to series and sum calculation. Based on the general formula we will answer…

Q: The sum of two positive numbers is 40. What are the numbers if their product is to be the largest. A…

A: let the two numbers be "x" and "y "x+y=40 → (1)F(x,y) = xyF(x)= x(40-x)F(x)=40x-x2differentiate…

Q: Consider the given: х3 — 4х2 x(х + 8)(х — 2) (x + 2)3 8(7x – 4) f(x) = ;f"(x) (x + 2)2 i f (x) : (x…

A: The given functions and their derivatives are: f(x)=x3-4x2(x+2)2=x2(x-4)(x+2)2,…

Q: 3. S(3Vx + dx 2 (x+3) + C

A: Topic = Integration As per guidelines , At a time only one question can be answered out of different…

Q: E- 100. This can be further simplifed to + y - 50

A: answer is in next step

Q: Use the Root Test to determine If the following series converges absolutely or diverges. Σ ne1 (3n +…

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Q: Use the chain rule to find the derivative of 4(6æ° – 2")" You do not need to expand out or multiply…

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Q: n f(x) = 3x³ + 2x 5 verify that f(x) is invertible and, if so, find the equation of the tangent line…

A: Topic:- application of derivatives

Q: 2. Using partial fractions, show that 4 Σ n² – 1 n=2 converges.

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Q: y = 4e" Vx et y = x2 – 1 x2 – 1

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Q: 1. Find the antiderivative of sin '(2.r)d.r.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: 20-21) What is the equation of the tangent line to y = x3 at x=2? A) y = x - 12 B) y = 12x C) y = x-…

A: Use derivative for finding the  equation of tangent line .

Q: Find. the Powier Series. and frad their Intervals and. sadif of. convergengeo If F(x)= g(x)= then…

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Q: A. For each of the following functions, find the indicated derivative using the definition. 1. f(x)…

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Q: 25 [x' sin xdx 27 |x' sin xdx 29 x’ sin xdx

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Q: Find the net area and the area of the region bounded by y= 11 cos x and the x-axis between x= -: and…

A: Area A = ∫ f(x)dx here limit from -π/2 to π A = ∫-π/2π cosxdx A = [sinx]-π/2π  A = sinπ - sin(-π/2)…

Q: The limit represents f '(c) for a function f(x) and a number c. Find f(x) and c. 2 Vx - 10 lim x- 25…

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Q: f(x) = e2x

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Q: (2x- 1)dx, n = 4 Calculate the Riemann sum of the integral using the given value of n.

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Q: x²-3x-4 if x>-1 x- 4 if x < -1 10.Why is f(x) = %3D x-4 discontinuous at x = -1?

A: Since this is a multiple question, according to the Bartleby answering rule, only first question is…

Q: Find the marginal revenue for producing x units. (The revenue is measured in dollars.) R = 30  10x −…

A: Given that, R = 30(10x − x3⁄2)

Q: f(x) = (x – 2)² 2. %3D

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Q: If f is a function and not necessarily a position function, then we can interpret AVa,a+h] as the…

A: This is a problem related to average and instantaneous rate of change of the function. Based on the…

Q: Solving a differential equation using the Laplace transform, you find Y(s)=L{y} to be Y(s)= − 48/s5…

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Q: ! Consider the nonhomogeneous DE: y" + y' - 6y = (12 – 16x)e*. A) Verify that y, = 4xe* is a…

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Q: A 5 meter long ladder is leaning against a wall. If the bottom of the ladder is being pushed towards…

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r=…

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Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. 00 2-1)nn…

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Q: 3. Find the equation of the tangent line to the curve y = x2 – 3x + 4 that is perpendicular to the…

A: As per the company's guidelines,  we are supposed to solve first question for you,  kindly repost…

Q: Use implicit differentiation to find an equation of the tangent line to the graph of the equation at…

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Q: a) Determine if the geometric series below is convergent or not. 107 -1 Σ n=1 3n +1 The series is…

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Q: Find the marginal cost for producing x units. (The cost is measured in dollars.) C = 300(6 + 5   x)…

A: We have to find the marginal cost

Q: 21 4 B=5 -2 A= %3D 3 0 Find the Lollowing 5 Only) (chease A+B 3A -B

A: A=2-130  , B=521-21) A+B    =2-130+521-2  =2+5-1+23+10-2  =714-2A+B=[714-2]

Q: 1. Determine whether the function ƒ(x) = x² + 6x +9 is continuous at x = -2. Sketch its graph…

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval  [a, b]. f(x) =…

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